线性代数 示例

表示为向量等式 4a-b-3c=27 , -4a-4b-2c=32 , 4a+9b+7c=37
, ,
解题步骤 1
以矩阵形式书写方程组。
解题步骤 2
求行简化阶梯形矩阵。
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解题步骤 2.1
Multiply each element of by to make the entry at a .
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解题步骤 2.1.1
Multiply each element of by to make the entry at a .
解题步骤 2.1.2
化简
解题步骤 2.2
Perform the row operation to make the entry at a .
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解题步骤 2.2.1
Perform the row operation to make the entry at a .
解题步骤 2.2.2
化简
解题步骤 2.3
Perform the row operation to make the entry at a .
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解题步骤 2.3.1
Perform the row operation to make the entry at a .
解题步骤 2.3.2
化简
解题步骤 2.4
Multiply each element of by to make the entry at a .
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解题步骤 2.4.1
Multiply each element of by to make the entry at a .
解题步骤 2.4.2
化简
解题步骤 2.5
Perform the row operation to make the entry at a .
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解题步骤 2.5.1
Perform the row operation to make the entry at a .
解题步骤 2.5.2
化简
解题步骤 2.6
Multiply each element of by to make the entry at a .
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解题步骤 2.6.1
Multiply each element of by to make the entry at a .
解题步骤 2.6.2
化简
解题步骤 2.7
Perform the row operation to make the entry at a .
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解题步骤 2.7.1
Perform the row operation to make the entry at a .
解题步骤 2.7.2
化简
解题步骤 2.8
Perform the row operation to make the entry at a .
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解题步骤 2.8.1
Perform the row operation to make the entry at a .
解题步骤 2.8.2
化简
解题步骤 2.9
Perform the row operation to make the entry at a .
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解题步骤 2.9.1
Perform the row operation to make the entry at a .
解题步骤 2.9.2
化简
解题步骤 3
使用结果矩阵定义方程组的最终解。
解题步骤 4
在等式两边都加上
解题步骤 5
从等式两边同时减去
解题步骤 6
因为 ,所以没有解。
无解